LMFDB - Embedded newform 2013.2.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,2,Mod(1,2013)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2013.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$16.0738859269$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{11} - 5x^{10} + 48x^{9} - 173x^{7} + 29x^{6} + 281x^{5} - 41x^{4} - 201x^{3} + 8x^{2} + 49x + 8 $ x^12 - 5x^11 - 5x^10 + 48x^9 - 173x^7 + 29x^6 + 281x^5 - 41x^4 - 201x^3 + 8x^2 + 49x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.199068$ of defining polynomial
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.19907 q^{2} +1.00000 q^{3} -0.562235 q^{4} +0.908382 q^{5} -1.19907 q^{6} -2.10536 q^{7} +3.07229 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.19907 q^{2} +1.00000 q^{3} -0.562235 q^{4} +0.908382 q^{5} -1.19907 q^{6} -2.10536 q^{7} +3.07229 q^{8} +1.00000 q^{9} -1.08921 q^{10} +1.00000 q^{11} -0.562235 q^{12} -3.37799 q^{13} +2.52447 q^{14} +0.908382 q^{15} -2.55942 q^{16} +7.64323 q^{17} -1.19907 q^{18} -7.74429 q^{19} -0.510724 q^{20} -2.10536 q^{21} -1.19907 q^{22} -6.30400 q^{23} +3.07229 q^{24} -4.17484 q^{25} +4.05044 q^{26} +1.00000 q^{27} +1.18371 q^{28} +1.64510 q^{29} -1.08921 q^{30} +8.65505 q^{31} -3.07567 q^{32} +1.00000 q^{33} -9.16475 q^{34} -1.91247 q^{35} -0.562235 q^{36} -3.41860 q^{37} +9.28593 q^{38} -3.37799 q^{39} +2.79082 q^{40} -8.72651 q^{41} +2.52447 q^{42} +5.78367 q^{43} -0.562235 q^{44} +0.908382 q^{45} +7.55893 q^{46} -1.53539 q^{47} -2.55942 q^{48} -2.56744 q^{49} +5.00592 q^{50} +7.64323 q^{51} +1.89922 q^{52} +5.99777 q^{53} -1.19907 q^{54} +0.908382 q^{55} -6.46830 q^{56} -7.74429 q^{57} -1.97258 q^{58} -3.20946 q^{59} -0.510724 q^{60} -1.00000 q^{61} -10.3780 q^{62} -2.10536 q^{63} +8.80678 q^{64} -3.06851 q^{65} -1.19907 q^{66} +14.0670 q^{67} -4.29729 q^{68} -6.30400 q^{69} +2.29319 q^{70} -9.15136 q^{71} +3.07229 q^{72} -15.0315 q^{73} +4.09914 q^{74} -4.17484 q^{75} +4.35411 q^{76} -2.10536 q^{77} +4.05044 q^{78} -8.85454 q^{79} -2.32493 q^{80} +1.00000 q^{81} +10.4637 q^{82} -12.7017 q^{83} +1.18371 q^{84} +6.94297 q^{85} -6.93502 q^{86} +1.64510 q^{87} +3.07229 q^{88} +7.46226 q^{89} -1.08921 q^{90} +7.11190 q^{91} +3.54433 q^{92} +8.65505 q^{93} +1.84103 q^{94} -7.03477 q^{95} -3.07567 q^{96} -13.5063 q^{97} +3.07854 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 7 q^{2} + 12 q^{3} + 13 q^{4} - 7 q^{5} - 7 q^{6} - 15 q^{7} - 18 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q - 7 * q^2 + 12 * q^3 + 13 * q^4 - 7 * q^5 - 7 * q^6 - 15 * q^7 - 18 * q^8 + 12 * q^9	\( 12 q - 7 q^{2} + 12 q^{3} + 13 q^{4} - 7 q^{5} - 7 q^{6} - 15 q^{7} - 18 q^{8} + 12 q^{9} - 6 q^{10} + 12 q^{11} + 13 q^{12} - 11 q^{13} + 3 q^{14} - 7 q^{15} + 19 q^{16} - 33 q^{17} - 7 q^{18} - 24 q^{19} - 11 q^{20} - 15 q^{21} - 7 q^{22} - 9 q^{23} - 18 q^{24} + 11 q^{25} - 16 q^{26} + 12 q^{27} - 41 q^{28} - 16 q^{29} - 6 q^{30} + q^{31} - 28 q^{32} + 12 q^{33} + 32 q^{34} - 22 q^{35} + 13 q^{36} - 6 q^{37} + 12 q^{38} - 11 q^{39} + 26 q^{40} - 21 q^{41} + 3 q^{42} - 39 q^{43} + 13 q^{44} - 7 q^{45} - 18 q^{47} + 19 q^{48} + 31 q^{49} - 44 q^{50} - 33 q^{51} + 3 q^{52} - 14 q^{53} - 7 q^{54} - 7 q^{55} + 16 q^{56} - 24 q^{57} + 33 q^{58} - 23 q^{59} - 11 q^{60} - 12 q^{61} - 25 q^{62} - 15 q^{63} + 12 q^{64} - 29 q^{65} - 7 q^{66} - 96 q^{68} - 9 q^{69} + 44 q^{70} - 19 q^{71} - 18 q^{72} - 42 q^{73} + 38 q^{74} + 11 q^{75} + 11 q^{76} - 15 q^{77} - 16 q^{78} - 11 q^{79} - 44 q^{80} + 12 q^{81} - 14 q^{82} - 56 q^{83} - 41 q^{84} + 16 q^{85} - 18 q^{86} - 16 q^{87} - 18 q^{88} - 55 q^{89} - 6 q^{90} + 11 q^{91} - 4 q^{92} + q^{93} - 5 q^{94} + 15 q^{95} - 28 q^{96} - 7 q^{97} + 6 q^{98} + 12 q^{99}+O(q^{100}) \) 12 * q - 7 * q^2 + 12 * q^3 + 13 * q^4 - 7 * q^5 - 7 * q^6 - 15 * q^7 - 18 * q^8 + 12 * q^9 - 6 * q^10 + 12 * q^11 + 13 * q^12 - 11 * q^13 + 3 * q^14 - 7 * q^15 + 19 * q^16 - 33 * q^17 - 7 * q^18 - 24 * q^19 - 11 * q^20 - 15 * q^21 - 7 * q^22 - 9 * q^23 - 18 * q^24 + 11 * q^25 - 16 * q^26 + 12 * q^27 - 41 * q^28 - 16 * q^29 - 6 * q^30 + q^31 - 28 * q^32 + 12 * q^33 + 32 * q^34 - 22 * q^35 + 13 * q^36 - 6 * q^37 + 12 * q^38 - 11 * q^39 + 26 * q^40 - 21 * q^41 + 3 * q^42 - 39 * q^43 + 13 * q^44 - 7 * q^45 - 18 * q^47 + 19 * q^48 + 31 * q^49 - 44 * q^50 - 33 * q^51 + 3 * q^52 - 14 * q^53 - 7 * q^54 - 7 * q^55 + 16 * q^56 - 24 * q^57 + 33 * q^58 - 23 * q^59 - 11 * q^60 - 12 * q^61 - 25 * q^62 - 15 * q^63 + 12 * q^64 - 29 * q^65 - 7 * q^66 - 96 * q^68 - 9 * q^69 + 44 * q^70 - 19 * q^71 - 18 * q^72 - 42 * q^73 + 38 * q^74 + 11 * q^75 + 11 * q^76 - 15 * q^77 - 16 * q^78 - 11 * q^79 - 44 * q^80 + 12 * q^81 - 14 * q^82 - 56 * q^83 - 41 * q^84 + 16 * q^85 - 18 * q^86 - 16 * q^87 - 18 * q^88 - 55 * q^89 - 6 * q^90 + 11 * q^91 - 4 * q^92 + q^93 - 5 * q^94 + 15 * q^95 - 28 * q^96 - 7 * q^97 + 6 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.19907	−0.847869	−0.423935	−	0.905693i	$-0.639351\pi$
$2$	−1.19907	−0.847869	−0.423935	+	0.905693i	$0.639351\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.562235	−0.281117
$5$	0.908382	0.406241	0.203120	−	0.979154i	$-0.434892\pi$
$5$	0.908382	0.406241	0.203120	+	0.979154i	$0.434892\pi$
$6$	−1.19907	−0.489518
$7$	−2.10536	−0.795753	−0.397876	−	0.917439i	$-0.630253\pi$
$7$	−2.10536	−0.795753	−0.397876	+	0.917439i	$0.630253\pi$
$8$	3.07229	1.08622
$9$	1.00000	0.333333
$10$	−1.08921	−0.344439
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.562235	−0.162303
$13$	−3.37799	−0.936886	−0.468443	−	0.883494i	$-0.655185\pi$
$13$	−3.37799	−0.936886	−0.468443	+	0.883494i	$0.655185\pi$
$14$	2.52447	0.674694
$15$	0.908382	0.234543
$16$	−2.55942	−0.639856
$17$	7.64323	1.85375	0.926877	−	0.375364i	$-0.122482\pi$
$17$	7.64323	1.85375	0.926877	+	0.375364i	$0.122482\pi$
$18$	−1.19907	−0.282623
$19$	−7.74429	−1.77666	−0.888331	−	0.459204i	$-0.848135\pi$
$19$	−7.74429	−1.77666	−0.888331	+	0.459204i	$0.848135\pi$
$20$	−0.510724	−0.114201
$21$	−2.10536	−0.459428
$22$	−1.19907	−0.255642
$23$	−6.30400	−1.31448	−0.657238	−	0.753684i	$-0.728275\pi$
$23$	−6.30400	−1.31448	−0.657238	+	0.753684i	$0.728275\pi$
$24$	3.07229	0.627130
$25$	−4.17484	−0.834969
$26$	4.05044	0.794357
$27$	1.00000	0.192450
$28$	1.18371	0.223700
$29$	1.64510	0.305487	0.152743	−	0.988266i	$-0.451189\pi$
$29$	1.64510	0.305487	0.152743	+	0.988266i	$0.451189\pi$
$30$	−1.08921	−0.198862
$31$	8.65505	1.55449	0.777246	−	0.629196i	$-0.216616\pi$
$31$	8.65505	1.55449	0.777246	+	0.629196i	$0.216616\pi$
$32$	−3.07567	−0.543706
$33$	1.00000	0.174078
$34$	−9.16475	−1.57174
$35$	−1.91247	−0.323267
$36$	−0.562235	−0.0937058
$37$	−3.41860	−0.562015	−0.281007	−	0.959706i	$-0.590669\pi$
$37$	−3.41860	−0.562015	−0.281007	+	0.959706i	$0.590669\pi$
$38$	9.28593	1.50638
$39$	−3.37799	−0.540912
$40$	2.79082	0.441267
$41$	−8.72651	−1.36285	−0.681426	−	0.731887i	$-0.738640\pi$
$41$	−8.72651	−1.36285	−0.681426	+	0.731887i	$0.738640\pi$
$42$	2.52447	0.389535
$43$	5.78367	0.882002	0.441001	−	0.897507i	$-0.354624\pi$
$43$	5.78367	0.882002	0.441001	+	0.897507i	$0.354624\pi$
$44$	−0.562235	−0.0847601
$45$	0.908382	0.135414
$46$	7.55893	1.11450
$47$	−1.53539	−0.223959	−0.111979	−	0.993711i	$-0.535719\pi$
$47$	−1.53539	−0.223959	−0.111979	+	0.993711i	$0.535719\pi$
$48$	−2.55942	−0.369421
$49$	−2.56744	−0.366778
$50$	5.00592	0.707944
$51$	7.64323	1.07027
$52$	1.89922	0.263375
$53$	5.99777	0.823857	0.411928	−	0.911216i	$-0.364855\pi$
$53$	5.99777	0.823857	0.411928	+	0.911216i	$0.364855\pi$
$54$	−1.19907	−0.163173
$55$	0.908382	0.122486
$56$	−6.46830	−0.864363
$57$	−7.74429	−1.02576
$58$	−1.97258	−0.259013
$59$	−3.20946	−0.417836	−0.208918	−	0.977933i	$-0.566994\pi$
$59$	−3.20946	−0.417836	−0.208918	+	0.977933i	$0.566994\pi$
$60$	−0.510724	−0.0659342
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−10.3780	−1.31801
$63$	−2.10536	−0.265251
$64$	8.80678	1.10085
$65$	−3.06851	−0.380601
$66$	−1.19907	−0.147595
$67$	14.0670	1.71856	0.859279	−	0.511507i	$-0.170913\pi$
$67$	14.0670	1.71856	0.859279	+	0.511507i	$0.170913\pi$
$68$	−4.29729	−0.521123
$69$	−6.30400	−0.758913
$70$	2.29319	0.274088
$71$	−9.15136	−1.08607	−0.543034	−	0.839711i	$-0.682724\pi$
$71$	−9.15136	−1.08607	−0.543034	+	0.839711i	$0.682724\pi$
$72$	3.07229	0.362073
$73$	−15.0315	−1.75931	−0.879655	−	0.475613i	$-0.842226\pi$
$73$	−15.0315	−1.75931	−0.879655	+	0.475613i	$0.842226\pi$
$74$	4.09914	0.476515
$75$	−4.17484	−0.482069
$76$	4.35411	0.499451
$77$	−2.10536	−0.239928
$78$	4.05044	0.458622
$79$	−8.85454	−0.996213	−0.498107	−	0.867116i	$-0.665971\pi$
$79$	−8.85454	−0.996213	−0.498107	+	0.867116i	$0.665971\pi$
$80$	−2.32493	−0.259935
$81$	1.00000	0.111111
$82$	10.4637	1.15552
$83$	−12.7017	−1.39419	−0.697094	−	0.716980i	$-0.745524\pi$
$83$	−12.7017	−1.39419	−0.697094	+	0.716980i	$0.745524\pi$
$84$	1.18371	0.129153
$85$	6.94297	0.753070
$86$	−6.93502	−0.747822
$87$	1.64510	0.176373
$88$	3.07229	0.327508
$89$	7.46226	0.790998	0.395499	−	0.918466i	$-0.370572\pi$
$89$	7.46226	0.790998	0.395499	+	0.918466i	$0.370572\pi$
$90$	−1.08921	−0.114813
$91$	7.11190	0.745530
$92$	3.54433	0.369522
$93$	8.65505	0.897487
$94$	1.84103	0.189888
$95$	−7.03477	−0.721752
$96$	−3.07567	−0.313909
$97$	−13.5063	−1.37136	−0.685680	−	0.727903i	$-0.740495\pi$
$97$	−13.5063	−1.37136	−0.685680	+	0.727903i	$0.740495\pi$
$98$	3.07854	0.310980
$99$	1.00000	0.100504
$100$	2.34724	0.234724
$101$	0.607307	0.0604293	0.0302147	−	0.999543i	$-0.490381\pi$
$101$	0.607307	0.0604293	0.0302147	+	0.999543i	$0.490381\pi$
$102$	−9.16475	−0.907446
$103$	−10.5671	−1.04121	−0.520603	−	0.853799i	$-0.674293\pi$
$103$	−10.5671	−1.04121	−0.520603	+	0.853799i	$0.674293\pi$
$104$	−10.3782	−1.01766
$105$	−1.91247	−0.186638
$106$	−7.19174	−0.698523
$107$	−10.9050	−1.05422	−0.527111	−	0.849796i	$-0.676725\pi$
$107$	−10.9050	−1.05422	−0.527111	+	0.849796i	$0.676725\pi$
$108$	−0.562235	−0.0541011
$109$	15.5962	1.49385	0.746923	−	0.664910i	$-0.231530\pi$
$109$	15.5962	1.49385	0.746923	+	0.664910i	$0.231530\pi$
$110$	−1.08921	−0.103852
$111$	−3.41860	−0.324479
$112$	5.38851	0.509167
$113$	7.09759	0.667685	0.333842	−	0.942629i	$-0.391655\pi$
$113$	7.09759	0.667685	0.333842	+	0.942629i	$0.391655\pi$
$114$	9.28593	0.869707
$115$	−5.72644	−0.533993
$116$	−0.924930	−0.0858776
$117$	−3.37799	−0.312295
$118$	3.84836	0.354270
$119$	−16.0918	−1.47513
$120$	2.79082	0.254765
$121$	1.00000	0.0909091
$122$	1.19907	0.108559
$123$	−8.72651	−0.786843
$124$	−4.86617	−0.436995
$125$	−8.33426	−0.745439
$126$	2.52447	0.224898
$127$	2.71184	0.240637	0.120319	−	0.992735i	$-0.461608\pi$
$127$	2.71184	0.240637	0.120319	+	0.992735i	$0.461608\pi$
$128$	−4.40860	−0.389669
$129$	5.78367	0.509224
$130$	3.67935	0.322700
$131$	−12.7574	−1.11462	−0.557309	−	0.830305i	$-0.688166\pi$
$131$	−12.7574	−1.11462	−0.557309	+	0.830305i	$0.688166\pi$
$132$	−0.562235	−0.0489363
$133$	16.3045	1.41378
$134$	−16.8673	−1.45711
$135$	0.908382	0.0781810
$136$	23.4822	2.01359
$137$	5.71972	0.488669	0.244334	−	0.969691i	$-0.421431\pi$
$137$	5.71972	0.488669	0.244334	+	0.969691i	$0.421431\pi$
$138$	7.55893	0.643459
$139$	−21.4792	−1.82184	−0.910921	−	0.412580i	$-0.864628\pi$
$139$	−21.4792	−1.82184	−0.910921	+	0.412580i	$0.864628\pi$
$140$	1.07526	0.0908760
$141$	−1.53539	−0.129303
$142$	10.9731	0.920843
$143$	−3.37799	−0.282482
$144$	−2.55942	−0.213285
$145$	1.49437	0.124101
$146$	18.0239	1.49166
$147$	−2.56744	−0.211759
$148$	1.92206	0.157992
$149$	−4.16417	−0.341142	−0.170571	−	0.985345i	$-0.554561\pi$
$149$	−4.16417	−0.341142	−0.170571	+	0.985345i	$0.554561\pi$
$150$	5.00592	0.408732
$151$	−14.1700	−1.15314	−0.576571	−	0.817047i	$-0.695610\pi$
$151$	−14.1700	−1.15314	−0.576571	+	0.817047i	$0.695610\pi$
$152$	−23.7927	−1.92985
$153$	7.64323	0.617918
$154$	2.52447	0.203428
$155$	7.86209	0.631498
$156$	1.89922	0.152060
$157$	18.6077	1.48506	0.742529	−	0.669814i	$-0.233626\pi$
$157$	18.6077	1.48506	0.742529	+	0.669814i	$0.233626\pi$
$158$	10.6172	0.844659
$159$	5.99777	0.475654
$160$	−2.79388	−0.220876
$161$	13.2722	1.04600
$162$	−1.19907	−0.0942077
$163$	−10.5593	−0.827069	−0.413535	−	0.910488i	$-0.635706\pi$
$163$	−10.5593	−0.827069	−0.413535	+	0.910488i	$0.635706\pi$
$164$	4.90635	0.383121
$165$	0.908382	0.0707174
$166$	15.2302	1.18209
$167$	−3.28707	−0.254361	−0.127181	−	0.991880i	$-0.540593\pi$
$167$	−3.28707	−0.254361	−0.127181	+	0.991880i	$0.540593\pi$
$168$	−6.46830	−0.499040
$169$	−1.58917	−0.122244
$170$	−8.32509	−0.638505
$171$	−7.74429	−0.592221
$172$	−3.25178	−0.247946
$173$	−0.860887	−0.0654520	−0.0327260	−	0.999464i	$-0.510419\pi$
$173$	−0.860887	−0.0654520	−0.0327260	+	0.999464i	$0.510419\pi$
$174$	−1.97258	−0.149541
$175$	8.78956	0.664428
$176$	−2.55942	−0.192924
$177$	−3.20946	−0.241237
$178$	−8.94776	−0.670663
$179$	9.58509	0.716423	0.358212	−	0.933640i	$-0.383387\pi$
$179$	9.58509	0.716423	0.358212	+	0.933640i	$0.383387\pi$
$180$	−0.510724	−0.0380671
$181$	−6.40332	−0.475955	−0.237977	−	0.971271i	$-0.576484\pi$
$181$	−6.40332	−0.475955	−0.237977	+	0.971271i	$0.576484\pi$
$182$	−8.52766	−0.632112
$183$	−1.00000	−0.0739221
$184$	−19.3678	−1.42781
$185$	−3.10540	−0.228313
$186$	−10.3780	−0.760952
$187$	7.64323	0.558928
$188$	0.863247	0.0629588
$189$	−2.10536	−0.153143
$190$	8.43517	0.611952
$191$	−16.8705	−1.22070	−0.610351	−	0.792131i	$-0.708972\pi$
$191$	−16.8705	−1.22070	−0.610351	+	0.792131i	$0.708972\pi$
$192$	8.80678	0.635575
$193$	−25.6621	−1.84720	−0.923599	−	0.383361i	$-0.874766\pi$
$193$	−25.6621	−1.84720	−0.923599	+	0.383361i	$0.874766\pi$
$194$	16.1950	1.16273
$195$	−3.06851	−0.219740
$196$	1.44351	0.103108
$197$	13.3689	0.952495	0.476247	−	0.879311i	$-0.341997\pi$
$197$	13.3689	0.952495	0.476247	+	0.879311i	$0.341997\pi$
$198$	−1.19907	−0.0852141
$199$	18.9929	1.34637	0.673187	−	0.739472i	$-0.264925\pi$
$199$	18.9929	1.34637	0.673187	+	0.739472i	$0.264925\pi$
$200$	−12.8263	−0.906960
$201$	14.0670	0.992210
$202$	−0.728203	−0.0512362
$203$	−3.46352	−0.243092
$204$	−4.29729	−0.300870
$205$	−7.92700	−0.553645
$206$	12.6707	0.882807
$207$	−6.30400	−0.438158
$208$	8.64571	0.599472
$209$	−7.74429	−0.535684
$210$	2.29319	0.158245
$211$	3.48077	0.239626	0.119813	−	0.992796i	$-0.461771\pi$
$211$	3.48077	0.239626	0.119813	+	0.992796i	$0.461771\pi$
$212$	−3.37215	−0.231601
$213$	−9.15136	−0.627041
$214$	13.0758	0.893843
$215$	5.25378	0.358305
$216$	3.07229	0.209043
$217$	−18.2220	−1.23699
$218$	−18.7009	−1.26659
$219$	−15.0315	−1.01574
$220$	−0.510724	−0.0344330
$221$	−25.8188	−1.73676
$222$	4.09914	0.275116
$223$	−10.5928	−0.709343	−0.354672	−	0.934991i	$-0.615407\pi$
$223$	−10.5928	−0.709343	−0.354672	+	0.934991i	$0.615407\pi$
$224$	6.47540	0.432656
$225$	−4.17484	−0.278323
$226$	−8.51049	−0.566109
$227$	−16.6648	−1.10608	−0.553042	−	0.833153i	$-0.686533\pi$
$227$	−16.6648	−1.10608	−0.553042	+	0.833153i	$0.686533\pi$
$228$	4.35411	0.288358
$229$	−0.484054	−0.0319872	−0.0159936	−	0.999872i	$-0.505091\pi$
$229$	−0.484054	−0.0319872	−0.0159936	+	0.999872i	$0.505091\pi$
$230$	6.86639	0.452756
$231$	−2.10536	−0.138523
$232$	5.05422	0.331826
$233$	−10.8458	−0.710532	−0.355266	−	0.934765i	$-0.615610\pi$
$233$	−10.8458	−0.710532	−0.355266	+	0.934765i	$0.615610\pi$
$234$	4.05044	0.264786
$235$	−1.39472	−0.0909812
$236$	1.80447	0.117461
$237$	−8.85454	−0.575164
$238$	19.2951	1.25072
$239$	−4.55377	−0.294559	−0.147279	−	0.989095i	$-0.547052\pi$
$239$	−4.55377	−0.294559	−0.147279	+	0.989095i	$0.547052\pi$
$240$	−2.32493	−0.150074
$241$	4.68562	0.301827	0.150914	−	0.988547i	$-0.451778\pi$
$241$	4.68562	0.301827	0.150914	+	0.988547i	$0.451778\pi$
$242$	−1.19907	−0.0770790
$243$	1.00000	0.0641500
$244$	0.562235	0.0359934
$245$	−2.33222	−0.149000
$246$	10.4637	0.667140
$247$	26.1601	1.66453
$248$	26.5909	1.68852
$249$	−12.7017	−0.804935
$250$	9.99335	0.632035
$251$	16.2561	1.02608	0.513038	−	0.858366i	$-0.328520\pi$
$251$	16.2561	1.02608	0.513038	+	0.858366i	$0.328520\pi$
$252$	1.18371	0.0745666
$253$	−6.30400	−0.396329
$254$	−3.25169	−0.204029
$255$	6.94297	0.434785
$256$	−12.3274	−0.770459
$257$	12.3649	0.771303	0.385652	−	0.922645i	$-0.373977\pi$
$257$	12.3649	0.771303	0.385652	+	0.922645i	$0.373977\pi$
$258$	−6.93502	−0.431755
$259$	7.19740	0.447225
$260$	1.72522	0.106994
$261$	1.64510	0.101829
$262$	15.2970	0.945051
$263$	9.17045	0.565474	0.282737	−	0.959197i	$-0.408758\pi$
$263$	9.17045	0.565474	0.282737	+	0.959197i	$0.408758\pi$
$264$	3.07229	0.189087
$265$	5.44826	0.334684
$266$	−19.5503	−1.19870
$267$	7.46226	0.456683
$268$	−7.90896	−0.483117
$269$	−14.0760	−0.858227	−0.429114	−	0.903250i	$-0.641174\pi$
$269$	−14.0760	−0.858227	−0.429114	+	0.903250i	$0.641174\pi$
$270$	−1.08921	−0.0662873
$271$	16.8400	1.02296	0.511479	−	0.859296i	$-0.329098\pi$
$271$	16.8400	1.02296	0.511479	+	0.859296i	$0.329098\pi$
$272$	−19.5622	−1.18614
$273$	7.11190	0.430432
$274$	−6.85834	−0.414327
$275$	−4.17484	−0.251753
$276$	3.54433	0.213344
$277$	13.4644	0.808997	0.404498	−	0.914539i	$-0.367446\pi$
$277$	13.4644	0.808997	0.404498	+	0.914539i	$0.367446\pi$
$278$	25.7550	1.54468
$279$	8.65505	0.518164
$280$	−5.87568	−0.351139
$281$	−6.62844	−0.395419	−0.197710	−	0.980261i	$-0.563350\pi$
$281$	−6.62844	−0.395419	−0.197710	+	0.980261i	$0.563350\pi$
$282$	1.84103	0.109632
$283$	−15.5157	−0.922313	−0.461156	−	0.887319i	$-0.652565\pi$
$283$	−15.5157	−0.922313	−0.461156	+	0.887319i	$0.652565\pi$
$284$	5.14522	0.305312
$285$	−7.03477	−0.416704
$286$	4.05044	0.239508
$287$	18.3725	1.08449
$288$	−3.07567	−0.181235
$289$	41.4189	2.43641
$290$	−1.79186	−0.105221
$291$	−13.5063	−0.791755
$292$	8.45126	0.494573
$293$	8.90220	0.520072	0.260036	−	0.965599i	$-0.416266\pi$
$293$	8.90220	0.520072	0.260036	+	0.965599i	$0.416266\pi$
$294$	3.07854	0.179544
$295$	−2.91541	−0.169742
$296$	−10.5030	−0.610472
$297$	1.00000	0.0580259
$298$	4.99312	0.289244
$299$	21.2949	1.23151
$300$	2.34724	0.135518
$301$	−12.1767	−0.701855
$302$	16.9909	0.977714
$303$	0.607307	0.0348889
$304$	19.8209	1.13681
$305$	−0.908382	−0.0520138
$306$	−9.16475	−0.523914
$307$	−23.6719	−1.35103	−0.675514	−	0.737347i	$-0.736078\pi$
$307$	−23.6719	−1.35103	−0.675514	+	0.737347i	$0.736078\pi$
$308$	1.18371	0.0674481
$309$	−10.5671	−0.601140
$310$	−9.42718	−0.535428
$311$	−22.9236	−1.29988	−0.649940	−	0.759985i	$-0.725206\pi$
$311$	−22.9236	−1.29988	−0.649940	+	0.759985i	$0.725206\pi$
$312$	−10.3782	−0.587549
$313$	0.810556	0.0458153	0.0229077	−	0.999738i	$-0.492708\pi$
$313$	0.810556	0.0458153	0.0229077	+	0.999738i	$0.492708\pi$
$314$	−22.3119	−1.25914
$315$	−1.91247	−0.107756
$316$	4.97833	0.280053
$317$	−26.2820	−1.47614	−0.738071	−	0.674723i	$-0.764263\pi$
$317$	−26.2820	−1.47614	−0.738071	+	0.674723i	$0.764263\pi$
$318$	−7.19174	−0.403293
$319$	1.64510	0.0921077
$320$	7.99992	0.447209
$321$	−10.9050	−0.608656
$322$	−15.9143	−0.886869
$323$	−59.1914	−3.29350
$324$	−0.562235	−0.0312353
$325$	14.1026	0.782271
$326$	12.6613	0.701247
$327$	15.5962	0.862473
$328$	−26.8104	−1.48036
$329$	3.23254	0.178216
$330$	−1.08921	−0.0599591
$331$	6.17943	0.339652	0.169826	−	0.985474i	$-0.445679\pi$
$331$	6.17943	0.339652	0.169826	+	0.985474i	$0.445679\pi$
$332$	7.14131	0.391931
$333$	−3.41860	−0.187338
$334$	3.94142	0.215665
$335$	12.7782	0.698148
$336$	5.38851	0.293968
$337$	6.31859	0.344196	0.172098	−	0.985080i	$-0.444945\pi$
$337$	6.31859	0.344196	0.172098	+	0.985080i	$0.444945\pi$
$338$	1.90553	0.103647
$339$	7.09759	0.385488
$340$	−3.90358	−0.211701
$341$	8.65505	0.468697
$342$	9.28593	0.502126
$343$	20.1429	1.08762
$344$	17.7691	0.958048
$345$	−5.72644	−0.308301
$346$	1.03226	0.0554948
$347$	−15.7380	−0.844858	−0.422429	−	0.906396i	$-0.638822\pi$
$347$	−15.7380	−0.844858	−0.422429	+	0.906396i	$0.638822\pi$
$348$	−0.924930	−0.0495815
$349$	−6.59365	−0.352950	−0.176475	−	0.984305i	$-0.556469\pi$
$349$	−6.59365	−0.352950	−0.176475	+	0.984305i	$0.556469\pi$
$350$	−10.5393	−0.563349
$351$	−3.37799	−0.180304
$352$	−3.07567	−0.163934
$353$	−19.3993	−1.03252	−0.516259	−	0.856432i	$-0.672676\pi$
$353$	−19.3993	−1.03252	−0.516259	+	0.856432i	$0.672676\pi$
$354$	3.84836	0.204538
$355$	−8.31293	−0.441205
$356$	−4.19554	−0.222363
$357$	−16.0918	−0.851667
$358$	−11.4932	−0.607433
$359$	16.3964	0.865370	0.432685	−	0.901545i	$-0.357566\pi$
$359$	16.3964	0.865370	0.432685	+	0.901545i	$0.357566\pi$
$360$	2.79082	0.147089
$361$	40.9740	2.15653
$362$	7.67802	0.403548
$363$	1.00000	0.0524864
$364$	−3.99856	−0.209581
$365$	−13.6544	−0.714703
$366$	1.19907	0.0626763
$367$	21.2245	1.10791	0.553954	−	0.832547i	$-0.313118\pi$
$367$	21.2245	1.10791	0.553954	+	0.832547i	$0.313118\pi$
$368$	16.1346	0.841074
$369$	−8.72651	−0.454284
$370$	3.72358	0.193580
$371$	−12.6275	−0.655586
$372$	−4.86617	−0.252299
$373$	3.47210	0.179778	0.0898892	−	0.995952i	$-0.471349\pi$
$373$	3.47210	0.179778	0.0898892	+	0.995952i	$0.471349\pi$
$374$	−9.16475	−0.473898
$375$	−8.33426	−0.430379
$376$	−4.71716	−0.243269
$377$	−5.55712	−0.286206
$378$	2.52447	0.129845
$379$	12.0509	0.619012	0.309506	−	0.950897i	$-0.399836\pi$
$379$	12.0509	0.619012	0.309506	+	0.950897i	$0.399836\pi$
$380$	3.95519	0.202897
$381$	2.71184	0.138932
$382$	20.2288	1.03500
$383$	14.4626	0.739005	0.369503	−	0.929230i	$-0.379528\pi$
$383$	14.4626	0.739005	0.369503	+	0.929230i	$0.379528\pi$
$384$	−4.40860	−0.224975
$385$	−1.91247	−0.0974687
$386$	30.7706	1.56618
$387$	5.78367	0.294001
$388$	7.59373	0.385513
$389$	−5.34623	−0.271065	−0.135532	−	0.990773i	$-0.543274\pi$
$389$	−5.34623	−0.271065	−0.135532	+	0.990773i	$0.543274\pi$
$390$	3.67935	0.186311
$391$	−48.1829	−2.43671
$392$	−7.88795	−0.398402
$393$	−12.7574	−0.643525
$394$	−16.0302	−0.807591
$395$	−8.04330	−0.404702
$396$	−0.562235	−0.0282534
$397$	4.16198	0.208884	0.104442	−	0.994531i	$-0.466694\pi$
$397$	4.16198	0.208884	0.104442	+	0.994531i	$0.466694\pi$
$398$	−22.7738	−1.14155
$399$	16.3045	0.816248
$400$	10.6852	0.534259
$401$	−15.1780	−0.757952	−0.378976	−	0.925407i	$-0.623724\pi$
$401$	−15.1780	−0.757952	−0.378976	+	0.925407i	$0.623724\pi$
$402$	−16.8673	−0.841265
$403$	−29.2367	−1.45638
$404$	−0.341449	−0.0169877
$405$	0.908382	0.0451378
$406$	4.15300	0.206110
$407$	−3.41860	−0.169454
$408$	23.4822	1.16254
$409$	−28.2603	−1.39738	−0.698691	−	0.715423i	$-0.746234\pi$
$409$	−28.2603	−1.39738	−0.698691	+	0.715423i	$0.746234\pi$
$410$	9.50501	0.469419
$411$	5.71972	0.282133
$412$	5.94118	0.292701
$413$	6.75707	0.332494
$414$	7.55893	0.371501
$415$	−11.5380	−0.566376
$416$	10.3896	0.509391
$417$	−21.4792	−1.05184
$418$	9.28593	0.454190
$419$	18.9263	0.924613	0.462306	−	0.886720i	$-0.347022\pi$
$419$	18.9263	0.924613	0.462306	+	0.886720i	$0.347022\pi$
$420$	1.07526	0.0524673
$421$	33.8543	1.64996	0.824980	−	0.565162i	$-0.191186\pi$
$421$	33.8543	1.64996	0.824980	+	0.565162i	$0.191186\pi$
$422$	−4.17368	−0.203171
$423$	−1.53539	−0.0746530
$424$	18.4269	0.894890
$425$	−31.9093	−1.54783
$426$	10.9731	0.531649
$427$	2.10536	0.101886
$428$	6.13115	0.296360
$429$	−3.37799	−0.163091
$430$	−6.29964	−0.303796
$431$	29.4506	1.41859	0.709294	−	0.704913i	$-0.249014\pi$
$431$	29.4506	1.41859	0.709294	+	0.704913i	$0.249014\pi$
$432$	−2.55942	−0.123140
$433$	23.4549	1.12717	0.563585	−	0.826058i	$-0.309422\pi$
$433$	23.4549	1.12717	0.563585	+	0.826058i	$0.309422\pi$
$434$	21.8495	1.04881
$435$	1.49437	0.0716498
$436$	−8.76873	−0.419946
$437$	48.8200	2.33538
$438$	18.0239	0.861213
$439$	8.43240	0.402456	0.201228	−	0.979544i	$-0.435507\pi$
$439$	8.43240	0.402456	0.201228	+	0.979544i	$0.435507\pi$
$440$	2.79082	0.133047
$441$	−2.56744	−0.122259
$442$	30.9585	1.47254
$443$	−2.90025	−0.137795	−0.0688975	−	0.997624i	$-0.521948\pi$
$443$	−2.90025	−0.137795	−0.0688975	+	0.997624i	$0.521948\pi$
$444$	1.92206	0.0912168
$445$	6.77858	0.321336
$446$	12.7014	0.601430
$447$	−4.16417	−0.196958
$448$	−18.5415	−0.876002
$449$	5.11415	0.241352	0.120676	−	0.992692i	$-0.461494\pi$
$449$	5.11415	0.241352	0.120676	+	0.992692i	$0.461494\pi$
$450$	5.00592	0.235981
$451$	−8.72651	−0.410915
$452$	−3.99051	−0.187698
$453$	−14.1700	−0.665767
$454$	19.9823	0.937815
$455$	6.46032	0.302864
$456$	−23.7927	−1.11420
$457$	37.8537	1.77072	0.885360	−	0.464905i	$-0.153912\pi$
$457$	37.8537	1.77072	0.885360	+	0.464905i	$0.153912\pi$
$458$	0.580414	0.0271210
$459$	7.64323	0.356755
$460$	3.21960	0.150115
$461$	37.2557	1.73517	0.867585	−	0.497289i	$-0.165671\pi$
$461$	37.2557	1.73517	0.867585	+	0.497289i	$0.165671\pi$
$462$	2.52447	0.117449
$463$	−15.9059	−0.739208	−0.369604	−	0.929189i	$-0.620507\pi$
$463$	−15.9059	−0.739208	−0.369604	+	0.929189i	$0.620507\pi$
$464$	−4.21049	−0.195467
$465$	7.86209	0.364596
$466$	13.0049	0.602438
$467$	22.9592	1.06243	0.531213	−	0.847238i	$-0.321736\pi$
$467$	22.9592	1.06243	0.531213	+	0.847238i	$0.321736\pi$
$468$	1.89922	0.0877917
$469$	−29.6162	−1.36755
$470$	1.67236	0.0771402
$471$	18.6077	0.857399
$472$	−9.86039	−0.453861
$473$	5.78367	0.265934
$474$	10.6172	0.487664
$475$	32.3312	1.48346
$476$	9.04736	0.414685
$477$	5.99777	0.274619
$478$	5.46028	0.249747
$479$	1.20360	0.0549939	0.0274969	−	0.999622i	$-0.491246\pi$
$479$	1.20360	0.0549939	0.0274969	+	0.999622i	$0.491246\pi$
$480$	−2.79388	−0.127523
$481$	11.5480	0.526544
$482$	−5.61838	−0.255910
$483$	13.2722	0.603907
$484$	−0.562235	−0.0255561
$485$	−12.2689	−0.557102
$486$	−1.19907	−0.0543908
$487$	1.33019	0.0602765	0.0301382	−	0.999546i	$-0.490405\pi$
$487$	1.33019	0.0602765	0.0301382	+	0.999546i	$0.490405\pi$
$488$	−3.07229	−0.139076
$489$	−10.5593	−0.477509
$490$	2.79649	0.126333
$491$	17.1036	0.771877	0.385938	−	0.922525i	$-0.373878\pi$
$491$	17.1036	0.771877	0.385938	+	0.922525i	$0.373878\pi$
$492$	4.90635	0.221195
$493$	12.5738	0.566297
$494$	−31.3678	−1.41130
$495$	0.908382	0.0408287
$496$	−22.1519	−0.994651
$497$	19.2669	0.864241
$498$	15.2302	0.682480
$499$	32.8982	1.47273	0.736363	−	0.676586i	$-0.236541\pi$
$499$	32.8982	1.47273	0.736363	+	0.676586i	$0.236541\pi$
$500$	4.68581	0.209556
$501$	−3.28707	−0.146855
$502$	−19.4922	−0.869979
$503$	−14.2163	−0.633873	−0.316937	−	0.948447i	$-0.602654\pi$
$503$	−14.2163	−0.633873	−0.316937	+	0.948447i	$0.602654\pi$
$504$	−6.46830	−0.288121
$505$	0.551667	0.0245488
$506$	7.55893	0.336035
$507$	−1.58917	−0.0705776
$508$	−1.52469	−0.0676473
$509$	−13.9837	−0.619819	−0.309909	−	0.950766i	$-0.600299\pi$
$509$	−13.9837	−0.619819	−0.309909	+	0.950766i	$0.600299\pi$
$510$	−8.32509	−0.368641
$511$	31.6469	1.39998
$512$	23.5985	1.04292
$513$	−7.74429	−0.341919
$514$	−14.8264	−0.653964
$515$	−9.59894	−0.422980
$516$	−3.25178	−0.143152
$517$	−1.53539	−0.0675262
$518$	−8.63018	−0.379188
$519$	−0.860887	−0.0377888
$520$	−9.42735	−0.413417
$521$	30.4960	1.33605	0.668026	−	0.744138i	$-0.267139\pi$
$521$	30.4960	1.33605	0.668026	+	0.744138i	$0.267139\pi$
$522$	−1.97258	−0.0863376
$523$	−27.8040	−1.21579	−0.607893	−	0.794019i	$-0.707985\pi$
$523$	−27.8040	−1.21579	−0.607893	+	0.794019i	$0.707985\pi$
$524$	7.17265	0.313339
$525$	8.78956	0.383608
$526$	−10.9960	−0.479448
$527$	66.1525	2.88165
$528$	−2.55942	−0.111385
$529$	16.7404	0.727845
$530$	−6.53284	−0.283768
$531$	−3.20946	−0.139279
$532$	−9.16698	−0.397439
$533$	29.4781	1.27684
$534$	−8.94776	−0.387208
$535$	−9.90587	−0.428268
$536$	43.2180	1.86673
$537$	9.58509	0.413627
$538$	16.8781	0.727665
$539$	−2.56744	−0.110588
$540$	−0.510724	−0.0219781
$541$	−14.8061	−0.636566	−0.318283	−	0.947996i	$-0.603106\pi$
$541$	−14.8061	−0.636566	−0.318283	+	0.947996i	$0.603106\pi$
$542$	−20.1923	−0.867335
$543$	−6.40332	−0.274793
$544$	−23.5080	−1.00790
$545$	14.1673	0.606861
$546$	−8.52766	−0.364950
$547$	24.0750	1.02937	0.514686	−	0.857379i	$-0.327908\pi$
$547$	24.0750	1.02937	0.514686	+	0.857379i	$0.327908\pi$
$548$	−3.21583	−0.137373
$549$	−1.00000	−0.0426790
$550$	5.00592	0.213453
$551$	−12.7401	−0.542746
$552$	−19.3678	−0.824346
$553$	18.6420	0.792739
$554$	−16.1447	−0.685924
$555$	−3.10540	−0.131817
$556$	12.0764	0.512152
$557$	19.7326	0.836095	0.418048	−	0.908425i	$-0.362714\pi$
$557$	19.7326	0.836095	0.418048	+	0.908425i	$0.362714\pi$
$558$	−10.3780	−0.439336
$559$	−19.5372	−0.826335
$560$	4.89483	0.206844
$561$	7.64323	0.322697
$562$	7.94795	0.335264
$563$	−23.4545	−0.988489	−0.494245	−	0.869323i	$-0.664555\pi$
$563$	−23.4545	−0.988489	−0.494245	+	0.869323i	$0.664555\pi$
$564$	0.863247	0.0363493
$565$	6.44732	0.271241
$566$	18.6044	0.782001
$567$	−2.10536	−0.0884170
$568$	−28.1157	−1.17971
$569$	15.3695	0.644322	0.322161	−	0.946685i	$-0.395591\pi$
$569$	15.3695	0.644322	0.322161	+	0.946685i	$0.395591\pi$
$570$	8.43517	0.353310
$571$	−19.9071	−0.833084	−0.416542	−	0.909116i	$-0.636758\pi$
$571$	−19.9071	−0.833084	−0.416542	+	0.909116i	$0.636758\pi$
$572$	1.89922	0.0794106
$573$	−16.8705	−0.704773
$574$	−22.0298	−0.919508
$575$	26.3182	1.09755
$576$	8.80678	0.366949
$577$	8.14776	0.339196	0.169598	−	0.985513i	$-0.445753\pi$
$577$	8.14776	0.339196	0.169598	+	0.985513i	$0.445753\pi$
$578$	−49.6641	−2.06576
$579$	−25.6621	−1.06648
$580$	−0.840189	−0.0348870
$581$	26.7416	1.10943
$582$	16.1950	0.671305
$583$	5.99777	0.248402
$584$	−46.1813	−1.91100
$585$	−3.06851	−0.126867
$586$	−10.6743	−0.440953
$587$	25.5926	1.05632	0.528159	−	0.849146i	$-0.322883\pi$
$587$	25.5926	1.05632	0.528159	+	0.849146i	$0.322883\pi$
$588$	1.44351	0.0595292
$589$	−67.0272	−2.76181
$590$	3.49578	0.143919
$591$	13.3689	0.549923
$592$	8.74965	0.359608
$593$	37.3368	1.53324	0.766620	−	0.642101i	$-0.221937\pi$
$593$	37.3368	1.53324	0.766620	+	0.642101i	$0.221937\pi$
$594$	−1.19907	−0.0491984
$595$	−14.6175	−0.599258
$596$	2.34124	0.0959010
$597$	18.9929	0.777329
$598$	−25.5340	−1.04416
$599$	8.65628	0.353686	0.176843	−	0.984239i	$-0.443412\pi$
$599$	8.65628	0.353686	0.176843	+	0.984239i	$0.443412\pi$
$600$	−12.8263	−0.523634
$601$	31.5825	1.28828	0.644139	−	0.764908i	$-0.277216\pi$
$601$	31.5825	1.28828	0.644139	+	0.764908i	$0.277216\pi$
$602$	14.6007	0.595082
$603$	14.0670	0.572853
$604$	7.96690	0.324168
$605$	0.908382	0.0369310
$606$	−0.728203	−0.0295812
$607$	37.8239	1.53523	0.767613	−	0.640913i	$-0.221444\pi$
$607$	37.8239	1.53523	0.767613	+	0.640913i	$0.221444\pi$
$608$	23.8189	0.965982
$609$	−3.46352	−0.140349
$610$	1.08921	0.0441009
$611$	5.18652	0.209824
$612$	−4.29729	−0.173708
$613$	−3.80620	−0.153731	−0.0768654	−	0.997041i	$-0.524491\pi$
$613$	−3.80620	−0.153731	−0.0768654	+	0.997041i	$0.524491\pi$
$614$	28.3843	1.14550
$615$	−7.92700	−0.319647
$616$	−6.46830	−0.260615
$617$	−16.8942	−0.680136	−0.340068	−	0.940401i	$-0.610450\pi$
$617$	−16.8942	−0.680136	−0.340068	+	0.940401i	$0.610450\pi$
$618$	12.6707	0.509689
$619$	−34.4938	−1.38642	−0.693212	−	0.720733i	$-0.743805\pi$
$619$	−34.4938	−1.38642	−0.693212	+	0.720733i	$0.743805\pi$
$620$	−4.42034	−0.177525
$621$	−6.30400	−0.252971
$622$	27.4870	1.10213
$623$	−15.7108	−0.629439
$624$	8.64571	0.346105
$625$	13.3035	0.532141
$626$	−0.971912	−0.0388454
$627$	−7.74429	−0.309277
$628$	−10.4619	−0.417476
$629$	−26.1292	−1.04184
$630$	2.29319	0.0913627
$631$	26.9008	1.07090	0.535452	−	0.844566i	$-0.320141\pi$
$631$	26.9008	1.07090	0.535452	+	0.844566i	$0.320141\pi$
$632$	−27.2038	−1.08211
$633$	3.48077	0.138348
$634$	31.5139	1.25158
$635$	2.46339	0.0977566
$636$	−3.37215	−0.133715
$637$	8.67281	0.343629
$638$	−1.97258	−0.0780953
$639$	−9.15136	−0.362022
$640$	−4.00469	−0.158299
$641$	−14.5218	−0.573577	−0.286788	−	0.957994i	$-0.592588\pi$
$641$	−14.5218	−0.573577	−0.286788	+	0.957994i	$0.592588\pi$
$642$	13.0758	0.516061
$643$	−3.94285	−0.155491	−0.0777454	−	0.996973i	$-0.524772\pi$
$643$	−3.94285	−0.155491	−0.0777454	+	0.996973i	$0.524772\pi$
$644$	−7.46210	−0.294048
$645$	5.25378	0.206867
$646$	70.9745	2.79245
$647$	43.9630	1.72836	0.864182	−	0.503179i	$-0.167836\pi$
$647$	43.9630	1.72836	0.864182	+	0.503179i	$0.167836\pi$
$648$	3.07229	0.120691
$649$	−3.20946	−0.125982
$650$	−16.9100	−0.663263
$651$	−18.2220	−0.714178
$652$	5.93681	0.232504
$653$	−4.05982	−0.158873	−0.0794366	−	0.996840i	$-0.525312\pi$
$653$	−4.05982	−0.158873	−0.0794366	+	0.996840i	$0.525312\pi$
$654$	−18.7009	−0.731264
$655$	−11.5886	−0.452803
$656$	22.3348	0.872028
$657$	−15.0315	−0.586436
$658$	−3.87604	−0.151104
$659$	−14.4508	−0.562925	−0.281463	−	0.959572i	$-0.590820\pi$
$659$	−14.4508	−0.562925	−0.281463	+	0.959572i	$0.590820\pi$
$660$	−0.510724	−0.0198799
$661$	8.34196	0.324465	0.162232	−	0.986753i	$-0.448131\pi$
$661$	8.34196	0.324465	0.162232	+	0.986753i	$0.448131\pi$
$662$	−7.40956	−0.287981
$663$	−25.8188	−1.00272
$664$	−39.0232	−1.51440
$665$	14.8107	0.574336
$666$	4.09914	0.158838
$667$	−10.3707	−0.401554
$668$	1.84811	0.0715054
$669$	−10.5928	−0.409540
$670$	−15.3219	−0.591938
$671$	−1.00000	−0.0386046
$672$	6.47540	0.249794
$673$	−10.3187	−0.397757	−0.198878	−	0.980024i	$-0.563730\pi$
$673$	−10.3187	−0.397757	−0.198878	+	0.980024i	$0.563730\pi$
$674$	−7.57643	−0.291833
$675$	−4.17484	−0.160690
$676$	0.893488	0.0343649
$677$	3.31247	0.127308	0.0636542	−	0.997972i	$-0.479725\pi$
$677$	3.31247	0.127308	0.0636542	+	0.997972i	$0.479725\pi$
$678$	−8.51049	−0.326843
$679$	28.4357	1.09126
$680$	21.3308	0.818000
$681$	−16.6648	−0.638598
$682$	−10.3780	−0.397394
$683$	−41.5744	−1.59080	−0.795400	−	0.606084i	$-0.792739\pi$
$683$	−41.5744	−1.59080	−0.795400	+	0.606084i	$0.792739\pi$
$684$	4.35411	0.166484
$685$	5.19569	0.198517
$686$	−24.1528	−0.922157
$687$	−0.484054	−0.0184678
$688$	−14.8029	−0.564354
$689$	−20.2604	−0.771860
$690$	6.86639	0.261399
$691$	−43.7146	−1.66298	−0.831491	−	0.555538i	$-0.812512\pi$
$691$	−43.7146	−1.66298	−0.831491	+	0.555538i	$0.812512\pi$
$692$	0.484021	0.0183997
$693$	−2.10536	−0.0799761
$694$	18.8709	0.716330
$695$	−19.5113	−0.740106
$696$	5.05422	0.191580
$697$	−66.6987	−2.52639
$698$	7.90624	0.299255
$699$	−10.8458	−0.410226
$700$	−4.94180	−0.186782
$701$	34.7177	1.31127	0.655634	−	0.755079i	$-0.272402\pi$
$701$	34.7177	1.31127	0.655634	+	0.755079i	$0.272402\pi$
$702$	4.05044	0.152874
$703$	26.4746	0.998510
$704$	8.80678	0.331918
$705$	−1.39472	−0.0525280
$706$	23.2610	0.875441
$707$	−1.27860	−0.0480868
$708$	1.80447	0.0678161
$709$	19.4137	0.729097	0.364549	−	0.931184i	$-0.381223\pi$
$709$	19.4137	0.729097	0.364549	+	0.931184i	$0.381223\pi$
$710$	9.96777	0.374084
$711$	−8.85454	−0.332071
$712$	22.9263	0.859198
$713$	−54.5614	−2.04334
$714$	19.2951	0.722102
$715$	−3.06851	−0.114756
$716$	−5.38907	−0.201399
$717$	−4.55377	−0.170064
$718$	−19.6604	−0.733721
$719$	−50.3050	−1.87606	−0.938031	−	0.346552i	$-0.887352\pi$
$719$	−50.3050	−1.87606	−0.938031	+	0.346552i	$0.887352\pi$
$720$	−2.32493	−0.0866451
$721$	22.2476	0.828542
$722$	−49.1306	−1.82845
$723$	4.68562	0.174260
$724$	3.60017	0.133799
$725$	−6.86801	−0.255072
$726$	−1.19907	−0.0445016
$727$	18.0509	0.669469	0.334735	−	0.942312i	$-0.391353\pi$
$727$	18.0509	0.669469	0.334735	+	0.942312i	$0.391353\pi$
$728$	21.8499	0.809810
$729$	1.00000	0.0370370
$730$	16.3725	0.605975
$731$	44.2059	1.63502
$732$	0.562235	0.0207808
$733$	−16.8360	−0.621850	−0.310925	−	0.950434i	$-0.600639\pi$
$733$	−16.8360	−0.621850	−0.310925	+	0.950434i	$0.600639\pi$
$734$	−25.4496	−0.939361
$735$	−2.33222	−0.0860252
$736$	19.3890	0.714688
$737$	14.0670	0.518165
$738$	10.4637	0.385173
$739$	−28.4551	−1.04674	−0.523368	−	0.852107i	$-0.675325\pi$
$739$	−28.4551	−1.04674	−0.523368	+	0.852107i	$0.675325\pi$
$740$	1.74596	0.0641828
$741$	26.1601	0.961017
$742$	15.1412	0.555852
$743$	−45.3705	−1.66448	−0.832240	−	0.554415i	$-0.812942\pi$
$743$	−45.3705	−1.66448	−0.832240	+	0.554415i	$0.812942\pi$
$744$	26.5909	0.974868
$745$	−3.78265	−0.138586
$746$	−4.16328	−0.152429
$747$	−12.7017	−0.464729
$748$	−4.29729	−0.157124
$749$	22.9589	0.838900
$750$	9.99335	0.364905
$751$	49.5115	1.80670	0.903351	−	0.428902i	$-0.141100\pi$
$751$	49.5115	1.80670	0.903351	+	0.428902i	$0.141100\pi$
$752$	3.92970	0.143301
$753$	16.2561	0.592406
$754$	6.66337	0.242665
$755$	−12.8718	−0.468453
$756$	1.18371	0.0430511
$757$	−13.4115	−0.487450	−0.243725	−	0.969844i	$-0.578370\pi$
$757$	−13.4115	−0.487450	−0.243725	+	0.969844i	$0.578370\pi$
$758$	−14.4498	−0.524842
$759$	−6.30400	−0.228821
$760$	−21.6129	−0.783982
$761$	−19.6883	−0.713700	−0.356850	−	0.934162i	$-0.616149\pi$
$761$	−19.6883	−0.713700	−0.356850	+	0.934162i	$0.616149\pi$
$762$	−3.25169	−0.117796
$763$	−32.8357	−1.18873
$764$	9.48516	0.343161
$765$	6.94297	0.251023
$766$	−17.3417	−0.626580
$767$	10.8415	0.391464
$768$	−12.3274	−0.444825
$769$	41.7710	1.50630	0.753151	−	0.657848i	$-0.228533\pi$
$769$	41.7710	1.50630	0.753151	+	0.657848i	$0.228533\pi$
$770$	2.29319	0.0826407
$771$	12.3649	0.445312
$772$	14.4281	0.519279
$773$	9.97424	0.358749	0.179374	−	0.983781i	$-0.442593\pi$
$773$	9.97424	0.358749	0.179374	+	0.983781i	$0.442593\pi$
$774$	−6.93502	−0.249274
$775$	−36.1335	−1.29795
$776$	−41.4954	−1.48960
$777$	7.19740	0.258205
$778$	6.41050	0.229827
$779$	67.5806	2.42133
$780$	1.72522	0.0617728
$781$	−9.15136	−0.327462
$782$	57.7746	2.06602
$783$	1.64510	0.0587909
$784$	6.57117	0.234685
$785$	16.9029	0.603291
$786$	15.2970	0.545625
$787$	−31.3612	−1.11791	−0.558954	−	0.829199i	$-0.688797\pi$
$787$	−31.3612	−1.11791	−0.558954	+	0.829199i	$0.688797\pi$
$788$	−7.51646	−0.267763
$789$	9.17045	0.326477
$790$	9.64447	0.343135
$791$	−14.9430	−0.531312
$792$	3.07229	0.109169
$793$	3.37799	0.119956
$794$	−4.99050	−0.177106
$795$	5.44826	0.193230
$796$	−10.6785	−0.378489
$797$	14.2403	0.504418	0.252209	−	0.967673i	$-0.418843\pi$
$797$	14.2403	0.504418	0.252209	+	0.967673i	$0.418843\pi$
$798$	−19.5503	−0.692072
$799$	−11.7353	−0.415165
$800$	12.8404	0.453978
$801$	7.46226	0.263666
$802$	18.1994	0.642644
$803$	−15.0315	−0.530452
$804$	−7.90896	−0.278928
$805$	12.0562	0.424926
$806$	35.0568	1.23482
$807$	−14.0760	−0.495498
$808$	1.86583	0.0656396
$809$	−22.0557	−0.775436	−0.387718	−	0.921778i	$-0.626737\pi$
$809$	−22.0557	−0.775436	−0.387718	+	0.921778i	$0.626737\pi$
$810$	−1.08921	−0.0382710
$811$	−5.25754	−0.184617	−0.0923086	−	0.995730i	$-0.529425\pi$
$811$	−5.25754	−0.184617	−0.0923086	+	0.995730i	$0.529425\pi$
$812$	1.94731	0.0683373
$813$	16.8400	0.590605
$814$	4.09914	0.143675
$815$	−9.59189	−0.335989
$816$	−19.5622	−0.684816
$817$	−44.7904	−1.56702
$818$	33.8861	1.18480
$819$	7.11190	0.248510
$820$	4.45683	0.155639
$821$	11.4406	0.399280	0.199640	−	0.979869i	$-0.436023\pi$
$821$	11.4406	0.399280	0.199640	+	0.979869i	$0.436023\pi$
$822$	−6.85834	−0.239212
$823$	−31.7442	−1.10653	−0.553266	−	0.833005i	$-0.686619\pi$
$823$	−31.7442	−1.10653	−0.553266	+	0.833005i	$0.686619\pi$
$824$	−32.4652	−1.13098
$825$	−4.17484	−0.145349
$826$	−8.10219	−0.281911
$827$	−37.8378	−1.31575	−0.657874	−	0.753128i	$-0.728544\pi$
$827$	−37.8378	−1.31575	−0.657874	+	0.753128i	$0.728544\pi$
$828$	3.54433	0.123174
$829$	24.1647	0.839276	0.419638	−	0.907691i	$-0.362157\pi$
$829$	24.1647	0.839276	0.419638	+	0.907691i	$0.362157\pi$
$830$	13.8348	0.480213
$831$	13.4644	0.467075
$832$	−29.7492	−1.03137
$833$	−19.6236	−0.679916
$834$	25.7550	0.891824
$835$	−2.98591	−0.103332
$836$	4.35411	0.150590
$837$	8.65505	0.299162
$838$	−22.6940	−0.783951
$839$	−6.00008	−0.207146	−0.103573	−	0.994622i	$-0.533027\pi$
$839$	−6.00008	−0.207146	−0.103573	+	0.994622i	$0.533027\pi$
$840$	−5.87568	−0.202730
$841$	−26.2937	−0.906678
$842$	−40.5937	−1.39895
$843$	−6.62844	−0.228296
$844$	−1.95701	−0.0673630
$845$	−1.44357	−0.0496605
$846$	1.84103	0.0632960
$847$	−2.10536	−0.0723411
$848$	−15.3508	−0.527149
$849$	−15.5157	−0.532498
$850$	38.2614	1.31236
$851$	21.5509	0.738755
$852$	5.14522	0.176272
$853$	8.02061	0.274621	0.137310	−	0.990528i	$-0.456154\pi$
$853$	8.02061	0.274621	0.137310	+	0.990528i	$0.456154\pi$
$854$	−2.52447	−0.0863858
$855$	−7.03477	−0.240584
$856$	−33.5033	−1.14512
$857$	1.57692	0.0538666	0.0269333	−	0.999637i	$-0.491426\pi$
$857$	1.57692	0.0538666	0.0269333	+	0.999637i	$0.491426\pi$
$858$	4.05044	0.138280
$859$	−0.00551133	−0.000188044 0	−9.40221e−5	−	1.00000i	$-0.500030\pi$
$859$	−0.00551133	−0.000188044 0	−9.40221e−5		1.00000i	$0.500030\pi$
$860$	−2.95386	−0.100726
$861$	18.3725	0.626132
$862$	−35.3133	−1.20278
$863$	43.4759	1.47994	0.739968	−	0.672642i	$-0.234841\pi$
$863$	43.4759	1.47994	0.739968	+	0.672642i	$0.234841\pi$
$864$	−3.07567	−0.104636
$865$	−0.782014	−0.0265893
$866$	−28.1240	−0.955693
$867$	41.4189	1.40666
$868$	10.2451	0.347740
$869$	−8.85454	−0.300370
$870$	−1.79186	−0.0607496
$871$	−47.5182	−1.61009
$872$	47.9162	1.62265
$873$	−13.5063	−0.457120
$874$	−58.5385	−1.98010
$875$	17.5466	0.593185
$876$	8.45126	0.285542
$877$	−50.9731	−1.72124	−0.860620	−	0.509249i	$-0.829923\pi$
$877$	−50.9731	−1.72124	−0.860620	+	0.509249i	$0.829923\pi$
$878$	−10.1110	−0.341230
$879$	8.90220	0.300264
$880$	−2.32493	−0.0783734
$881$	−11.0214	−0.371322	−0.185661	−	0.982614i	$-0.559443\pi$
$881$	−11.0214	−0.371322	−0.185661	+	0.982614i	$0.559443\pi$
$882$	3.07854	0.103660
$883$	−2.14140	−0.0720637	−0.0360319	−	0.999351i	$-0.511472\pi$
$883$	−2.14140	−0.0720637	−0.0360319	+	0.999351i	$0.511472\pi$
$884$	14.5162	0.488233
$885$	−2.91541	−0.0980004
$886$	3.47760	0.116832
$887$	−31.6725	−1.06346	−0.531729	−	0.846914i	$-0.678458\pi$
$887$	−31.6725	−1.06346	−0.531729	+	0.846914i	$0.678458\pi$
$888$	−10.5030	−0.352456
$889$	−5.70942	−0.191488
$890$	−8.12798	−0.272451
$891$	1.00000	0.0335013
$892$	5.95562	0.199409
$893$	11.8905	0.397899
$894$	4.99312	0.166995
$895$	8.70692	0.291040
$896$	9.28170	0.310080
$897$	21.2949	0.711015
$898$	−6.13222	−0.204635
$899$	14.2384	0.474877
$900$	2.34724	0.0782414
$901$	45.8423	1.52723
$902$	10.4637	0.348402
$903$	−12.1767	−0.405216
$904$	21.8059	0.725253
$905$	−5.81666	−0.193352
$906$	16.9909	0.564483
$907$	−8.56188	−0.284293	−0.142146	−	0.989846i	$-0.545400\pi$
$907$	−8.56188	−0.284293	−0.142146	+	0.989846i	$0.545400\pi$
$908$	9.36955	0.310939
$909$	0.607307	0.0201431
$910$	−7.74636	−0.256789
$911$	−43.1233	−1.42874	−0.714370	−	0.699768i	$-0.753287\pi$
$911$	−43.1233	−1.42874	−0.714370	+	0.699768i	$0.753287\pi$
$912$	19.8209	0.656336
$913$	−12.7017	−0.420363
$914$	−45.3892	−1.50134
$915$	−0.908382	−0.0300302
$916$	0.272152	0.00899216
$917$	26.8589	0.886961
$918$	−9.16475	−0.302482
$919$	−20.1220	−0.663764	−0.331882	−	0.943321i	$-0.607684\pi$
$919$	−20.1220	−0.663764	−0.331882	+	0.943321i	$0.607684\pi$
$920$	−17.5933	−0.580034
$921$	−23.6719	−0.780017
$922$	−44.6721	−1.47120
$923$	30.9132	1.01752
$924$	1.18371	0.0389412
$925$	14.2721	0.469265
$926$	19.0722	0.626752
$927$	−10.5671	−0.347069
$928$	−5.05977	−0.166095
$929$	−22.3300	−0.732622	−0.366311	−	0.930492i	$-0.619379\pi$
$929$	−22.3300	−0.732622	−0.366311	+	0.930492i	$0.619379\pi$
$930$	−9.42718	−0.309129
$931$	19.8830	0.651640
$932$	6.09788	0.199743
$933$	−22.9236	−0.750486
$934$	−27.5297	−0.900799
$935$	6.94297	0.227059
$936$	−10.3782	−0.339222
$937$	−10.7662	−0.351716	−0.175858	−	0.984416i	$-0.556270\pi$
$937$	−10.7662	−0.351716	−0.175858	+	0.984416i	$0.556270\pi$
$938$	35.5118	1.15950
$939$	0.810556	0.0264515
$940$	0.784158	0.0255764
$941$	14.5407	0.474015	0.237007	−	0.971508i	$-0.423833\pi$
$941$	14.5407	0.474015	0.237007	+	0.971508i	$0.423833\pi$
$942$	−22.3119	−0.726962
$943$	55.0119	1.79143
$944$	8.21435	0.267354
$945$	−1.91247	−0.0622128
$946$	−6.93502	−0.225477
$947$	24.6200	0.800042	0.400021	−	0.916506i	$-0.369003\pi$
$947$	24.6200	0.800042	0.400021	+	0.916506i	$0.369003\pi$
$948$	4.97833	0.161689
$949$	50.7764	1.64827
$950$	−38.7673	−1.25778
$951$	−26.2820	−0.852251
$952$	−49.4387	−1.60232
$953$	−27.3458	−0.885818	−0.442909	−	0.896567i	$-0.646054\pi$
$953$	−27.3458	−0.885818	−0.442909	+	0.896567i	$0.646054\pi$
$954$	−7.19174	−0.232841
$955$	−15.3248	−0.495899
$956$	2.56029	0.0828056
$957$	1.64510	0.0531784
$958$	−1.44320	−0.0466276
$959$	−12.0421	−0.388860
$960$	7.99992	0.258196
$961$	43.9099	1.41645
$962$	−13.8469	−0.446441
$963$	−10.9050	−0.351407
$964$	−2.63442	−0.0848489
$965$	−23.3110	−0.750406
$966$	−15.9143	−0.512034
$967$	2.18065	0.0701250	0.0350625	−	0.999385i	$-0.488837\pi$
$967$	2.18065	0.0701250	0.0350625	+	0.999385i	$0.488837\pi$
$968$	3.07229	0.0987473
$969$	−59.1914	−1.90150
$970$	14.7113	0.472350
$971$	−13.6991	−0.439624	−0.219812	−	0.975542i	$-0.570544\pi$
$971$	−13.6991	−0.439624	−0.219812	+	0.975542i	$0.570544\pi$
$972$	−0.562235	−0.0180337
$973$	45.2215	1.44974
$974$	−1.59498	−0.0511066
$975$	14.1026	0.451644
$976$	2.55942	0.0819251
$977$	2.42926	0.0777189	0.0388594	−	0.999245i	$-0.487628\pi$
$977$	2.42926	0.0777189	0.0388594	+	0.999245i	$0.487628\pi$
$978$	12.6613	0.404865
$979$	7.46226	0.238495
$980$	1.31126	0.0418865
$981$	15.5962	0.497949
$982$	−20.5084	−0.654451
$983$	−10.3247	−0.329308	−0.164654	−	0.986351i	$-0.552651\pi$
$983$	−10.3247	−0.329308	−0.164654	+	0.986351i	$0.552651\pi$
$984$	−26.8104	−0.854684
$985$	12.1441	0.386942
$986$	−15.0769	−0.480146
$987$	3.23254	0.102893
$988$	−14.7081	−0.467928
$989$	−36.4603	−1.15937
$990$	−1.08921	−0.0346174
$991$	19.4525	0.617930	0.308965	−	0.951073i	$-0.400017\pi$
$991$	19.4525	0.617930	0.308965	+	0.951073i	$0.400017\pi$
$992$	−26.6201	−0.845188
$993$	6.17943	0.196098
$994$	−23.1024	−0.732763
$995$	17.2528	0.546952
$996$	7.14131	0.226281
$997$	−29.3654	−0.930012	−0.465006	−	0.885308i	$-0.653948\pi$
$997$	−29.3654	−0.930012	−0.465006	+	0.885308i	$0.653948\pi$
$998$	−39.4472	−1.24868
$999$	−3.41860	−0.108160

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.c.1.6	✓	12
3.2	odd	2		6039.2.a.f.1.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.c.1.6	✓	12	1.1	even	1	trivial
6039.2.a.f.1.7		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-1.19907 q^{2} +1.00000 q^{3} -0.562235 q^{4} +0.908382 q^{5} -1.19907 q^{6} -2.10536 q^{7} +3.07229 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.19907 q^{2} +1.00000 q^{3} -0.562235 q^{4} +0.908382 q^{5} -1.19907 q^{6} -2.10536 q^{7} +3.07229 q^{8} +1.00000 q^{9} -1.08921 q^{10} +1.00000 q^{11} -0.562235 q^{12} -3.37799 q^{13} +2.52447 q^{14} +0.908382 q^{15} -2.55942 q^{16} +7.64323 q^{17} -1.19907 q^{18} -7.74429 q^{19} -0.510724 q^{20} -2.10536 q^{21} -1.19907 q^{22} -6.30400 q^{23} +3.07229 q^{24} -4.17484 q^{25} +4.05044 q^{26} +1.00000 q^{27} +1.18371 q^{28} +1.64510 q^{29} -1.08921 q^{30} +8.65505 q^{31} -3.07567 q^{32} +1.00000 q^{33} -9.16475 q^{34} -1.91247 q^{35} -0.562235 q^{36} -3.41860 q^{37} +9.28593 q^{38} -3.37799 q^{39} +2.79082 q^{40} -8.72651 q^{41} +2.52447 q^{42} +5.78367 q^{43} -0.562235 q^{44} +0.908382 q^{45} +7.55893 q^{46} -1.53539 q^{47} -2.55942 q^{48} -2.56744 q^{49} +5.00592 q^{50} +7.64323 q^{51} +1.89922 q^{52} +5.99777 q^{53} -1.19907 q^{54} +0.908382 q^{55} -6.46830 q^{56} -7.74429 q^{57} -1.97258 q^{58} -3.20946 q^{59} -0.510724 q^{60} -1.00000 q^{61} -10.3780 q^{62} -2.10536 q^{63} +8.80678 q^{64} -3.06851 q^{65} -1.19907 q^{66} +14.0670 q^{67} -4.29729 q^{68} -6.30400 q^{69} +2.29319 q^{70} -9.15136 q^{71} +3.07229 q^{72} -15.0315 q^{73} +4.09914 q^{74} -4.17484 q^{75} +4.35411 q^{76} -2.10536 q^{77} +4.05044 q^{78} -8.85454 q^{79} -2.32493 q^{80} +1.00000 q^{81} +10.4637 q^{82} -12.7017 q^{83} +1.18371 q^{84} +6.94297 q^{85} -6.93502 q^{86} +1.64510 q^{87} +3.07229 q^{88} +7.46226 q^{89} -1.08921 q^{90} +7.11190 q^{91} +3.54433 q^{92} +8.65505 q^{93} +1.84103 q^{94} -7.03477 q^{95} -3.07567 q^{96} -13.5063 q^{97} +3.07854 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 7 q^{2} + 12 q^{3} + 13 q^{4} - 7 q^{5} - 7 q^{6} - 15 q^{7} - 18 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q - 7 * q^2 + 12 * q^3 + 13 * q^4 - 7 * q^5 - 7 * q^6 - 15 * q^7 - 18 * q^8 + 12 * q^9	\( 12 q - 7 q^{2} + 12 q^{3} + 13 q^{4} - 7 q^{5} - 7 q^{6} - 15 q^{7} - 18 q^{8} + 12 q^{9} - 6 q^{10} + 12 q^{11} + 13 q^{12} - 11 q^{13} + 3 q^{14} - 7 q^{15} + 19 q^{16} - 33 q^{17} - 7 q^{18} - 24 q^{19} - 11 q^{20} - 15 q^{21} - 7 q^{22} - 9 q^{23} - 18 q^{24} + 11 q^{25} - 16 q^{26} + 12 q^{27} - 41 q^{28} - 16 q^{29} - 6 q^{30} + q^{31} - 28 q^{32} + 12 q^{33} + 32 q^{34} - 22 q^{35} + 13 q^{36} - 6 q^{37} + 12 q^{38} - 11 q^{39} + 26 q^{40} - 21 q^{41} + 3 q^{42} - 39 q^{43} + 13 q^{44} - 7 q^{45} - 18 q^{47} + 19 q^{48} + 31 q^{49} - 44 q^{50} - 33 q^{51} + 3 q^{52} - 14 q^{53} - 7 q^{54} - 7 q^{55} + 16 q^{56} - 24 q^{57} + 33 q^{58} - 23 q^{59} - 11 q^{60} - 12 q^{61} - 25 q^{62} - 15 q^{63} + 12 q^{64} - 29 q^{65} - 7 q^{66} - 96 q^{68} - 9 q^{69} + 44 q^{70} - 19 q^{71} - 18 q^{72} - 42 q^{73} + 38 q^{74} + 11 q^{75} + 11 q^{76} - 15 q^{77} - 16 q^{78} - 11 q^{79} - 44 q^{80} + 12 q^{81} - 14 q^{82} - 56 q^{83} - 41 q^{84} + 16 q^{85} - 18 q^{86} - 16 q^{87} - 18 q^{88} - 55 q^{89} - 6 q^{90} + 11 q^{91} - 4 q^{92} + q^{93} - 5 q^{94} + 15 q^{95} - 28 q^{96} - 7 q^{97} + 6 q^{98} + 12 q^{99}+O(q^{100}) \) 12 * q - 7 * q^2 + 12 * q^3 + 13 * q^4 - 7 * q^5 - 7 * q^6 - 15 * q^7 - 18 * q^8 + 12 * q^9 - 6 * q^10 + 12 * q^11 + 13 * q^12 - 11 * q^13 + 3 * q^14 - 7 * q^15 + 19 * q^16 - 33 * q^17 - 7 * q^18 - 24 * q^19 - 11 * q^20 - 15 * q^21 - 7 * q^22 - 9 * q^23 - 18 * q^24 + 11 * q^25 - 16 * q^26 + 12 * q^27 - 41 * q^28 - 16 * q^29 - 6 * q^30 + q^31 - 28 * q^32 + 12 * q^33 + 32 * q^34 - 22 * q^35 + 13 * q^36 - 6 * q^37 + 12 * q^38 - 11 * q^39 + 26 * q^40 - 21 * q^41 + 3 * q^42 - 39 * q^43 + 13 * q^44 - 7 * q^45 - 18 * q^47 + 19 * q^48 + 31 * q^49 - 44 * q^50 - 33 * q^51 + 3 * q^52 - 14 * q^53 - 7 * q^54 - 7 * q^55 + 16 * q^56 - 24 * q^57 + 33 * q^58 - 23 * q^59 - 11 * q^60 - 12 * q^61 - 25 * q^62 - 15 * q^63 + 12 * q^64 - 29 * q^65 - 7 * q^66 - 96 * q^68 - 9 * q^69 + 44 * q^70 - 19 * q^71 - 18 * q^72 - 42 * q^73 + 38 * q^74 + 11 * q^75 + 11 * q^76 - 15 * q^77 - 16 * q^78 - 11 * q^79 - 44 * q^80 + 12 * q^81 - 14 * q^82 - 56 * q^83 - 41 * q^84 + 16 * q^85 - 18 * q^86 - 16 * q^87 - 18 * q^88 - 55 * q^89 - 6 * q^90 + 11 * q^91 - 4 * q^92 + q^93 - 5 * q^94 + 15 * q^95 - 28 * q^96 - 7 * q^97 + 6 * q^98 + 12 * q^99

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